Results 1 to 10 of about 2,026 (229)

Uncertainty quantification and weak approximation of an elliptic inverse problem [PDF]

, 2011
We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a linear uniformly elliptic partial differential equation ...
Worthington, Claire, Robinson, Stewart, Davis, Neil D., Radnor, Zoe, Cooke, Matthew W, Burgess, Nicola, Cooke, Matthew, M. Dashti, Davies, Neil, Dashti, M., A. M. Stuart, Masoumeh Dashti (4463344), Worthington, Claire H, A M Stuart (13396491), Stuart, A. M.   +14 more
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The General Fractional Derivative and Related Fractional Differential Equations

Mathematics, 2020
In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine ...
Yuri Luchko, Masahiro Yamamoto
doaj   +1 more source

Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

International Journal of Mathematics and Mathematical Sciences, 2014
Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction
Nemat Dalir
doaj   +1 more source

A Second-Order Network Structure Based on Gradient-Enhanced Physics-Informed Neural Networks for Solving Parabolic Partial Differential Equations

Entropy, 2023
Physics-informed neural networks (PINNs) are effective for solving partial differential equations (PDEs). This method of embedding partial differential equations and their initial boundary conditions into the loss functions of neural networks has ...
Kuo Sun, Xinlong Feng
doaj   +1 more source

The RBF-FD and RBF-FDTD Methods for Solving Time-Domain Electrical Transient Problems in Power Systems

International Transactions on Electrical Energy Systems, 2023
In this paper, the development and application of the radial basis function-finite difference (RBF-FD) method and the RBF-finite difference time domain (RBF-FDTD) method for solving electrical transient problems in power systems that are defined by the ...
Duc-Quang Vu, Nhat-Nam Nguyen, Phan-Tu Vu   +2 more
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Solving Inverse Source Problems for linear PDEs using Sparse Sensor Measurements [PDF]

, 2016
Many physical phenomena across several applications can be described by partial differential equations (PDEs). In these applications, sensors collect sparse samples of the resulting phenomena with the aim of detecting its cause/source, using some ...
Pier Luigi Dragotti, Dragotti, PL, Murray-Bruce, J, John Murray-Bruce   +3 more
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Fully probabilistic deep models for forward and inverse problems in parametric PDEs

, 2023
We introduce a physics-driven deep latent variable model (PDDLVM) to learn simultaneously parameter-to-solution (forward) and solution-to-parameter (inverse) maps of parametric partial differential equations (PDEs). Our formulation leverages conventional
Arnaud Vadeboncoeur, Fehmi Cirak, Vadeboncoeur, Arnaud, Ieva Kazlauskaite, Kazlauskaite, Ieva, Cirak, Fehmi, Ömer Deniz Akyildiz, Mark Girolami, Akyildiz, Ömer Deniz, Girolami, Mark   +9 more
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Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations [PDF]

, 2010
A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani et al. (Automatica 46(10), 1616-1625, 2010 ).
Karim Ramdani, Ghislain Haine, Haine, Ghislain, Ramdani, Karim   +3 more
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Numerical methods for boundary value problems on random domains [PDF]

, 2014
In this thesis, we consider the numerical solution of elliptic boundary value problems on random domains. The underlying domain is modelled via a random vector field which is given by its mean and its covariance.
Peters, Michael
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Gradient Statistics-Based Multi-Objective Optimization in Physics-Informed Neural Networks

Sensors, 2023
Modeling and simulation of complex non-linear systems are essential in physics, engineering, and signal processing. Neural networks are widely regarded for such tasks due to their ability to learn complex representations from data.
Sai Karthikeya Vemuri, Joachim Denzler
doaj   +1 more source